The first two entries of a sequence are 3 and 27. Starting from the third entry, every entry is the absolute value of the difference of the two previous entries. What is the 2016th entry of this sequence?
After listing it out, I got:
3, 27, 24, 3, 21, 18, 3, 15, 12, 3, 9, 6, 3, 3, 0, 3, 3, 0, 3, 3, 0... and so on, but I'm not quite sure what to do with that.
Help appreciated! :D
You're on the right track....we have a pattern that you found as
Term 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
3, 27, 24, 3, 21, 18, 3, 15, 12, 3, 9, 6, 3, [3, 0, 3] , [ 3, 0, 3], ]3, 0 , 3]
Notice that......starting with the 14th term we have the repeating pattern 3,0,3
Notice that after this ( term number + 2) ] / 3 gives us what we need to determine the 2016th term
Notice that
(14 + 2) / 3 = 16/3 = 5 + 1/3 = 1st number in the pattern = 3
(15 + 2) / 3 = 17/3 = 5 + 2/3 = 2nd number in the pattern = 0
(16 + 2) / 3 = 18/3 = 6 whole number result gives us the 3rd number in the pattern = 3
So....to determine the 2016th term we have
(2016 + 2 ] / 3 = 2018 / 3 = = 672 + 2/3 = 2nd number in pattern = 0